Mathematics
Grade 5
15 min
Independent and dependent events
Independent and dependent events
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1
Introduction & Learning Objectives
Learning Objectives
Define an 'event' and an 'outcome' in a simple probability scenario.
Explain the difference between independent and dependent events using their own words.
Identify whether two events are independent or dependent in a given real-world scenario.
Explain how the concept of 'replacement' affects whether events are independent or dependent.
Provide at least one example of an independent event pair.
Provide at least one example of a dependent event pair.
If you flip a coin and get heads, are you more likely to get tails on the next flip? Let's find out! 🪙
In this lesson, we will explore two types of events: independent and dependent. You will learn how to tell if one event's outcome affects the outcome of another, whic...
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Key Concepts & Vocabulary
TermDefinitionExample
EventA specific thing that can happen, or a set of outcomes from an experiment.Flipping a coin and getting tails is an event. Rolling a 4 on a die is an event.
OutcomeA single possible result of an experiment or event.When you roll a standard six-sided die, the possible outcomes are 1, 2, 3, 4, 5, or 6.
Independent EventsTwo events where the outcome of the first event does NOT affect the outcome of the second event.Flipping a coin and getting heads (first event), and then rolling a die and getting a 5 (second event). The coin flip doesn't change the die roll.
Dependent EventsTwo events where the outcome of the first event DOES affect the outcome of the second event.Picking a blue marble from a bag (first event) and, without putting it back, picking a red marble...
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Core Formulas
The Independence Test
Event A outcome \nrightarrow Event B outcome
Use this test to see if events are independent. Ask yourself: 'Does the result of the first event change the possible outcomes or chances of the second event?' If the answer is NO, the events are independent.
The Dependence Test
Event A outcome \rightarrow Event B outcome
Use this test to see if events are dependent. Ask yourself: 'Does the result of the first event change the possible outcomes or chances of the second event?' If the answer is YES, the events are dependent. Look for keywords like 'without replacement'.
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Challenging
If the second of two events was affected by the first, this means the events were dependent. Which of the following must also be true?
A.The first item chosen was not replaced.
B.The first item chosen was replaced.
C.Both events had the same outcome.
D.The experiment involved a coin.
Challenging
A teacher picks one student from a class of 25 to be the line leader. Then, from the remaining students, she picks another student to be the caboose. Why are these events dependent?
A.Because being line leader is more important than being caboose.
B.Because the student chosen as line leader cannot also be chosen as caboose, which changes the pool of students for the second pick.
C.Because both students are from the same class.
D.Because the teacher might pick a boy first and then a girl.
Challenging
A spinner with four equal sections (Red, Blue, Green, Yellow) lands on 'Red' five times in a row. A student says, 'It's definitely going to land on a different color next time because it's tired of Red!' Why is this thinking incorrect?
A.Because the spinner might be broken and can only land on Red.
B.Because Red is the luckiest color.
C.Because each spin is an independent event and the spinner has no memory of past results.
D.Because the student should spin it ten times to be sure.
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